Related papers: High-order schemes for the Euler equations in cyli…
We present a novel approach for high-order accurate numerical differentiation on unstructured meshes of quadrilateral elements. To differentiate a given function, an auxiliary function with greater smoothness properties is defined which…
A new Essentially Non-oscillatory (ENO) recovery algorithm is developed and tested in a Finite Volume method. The construction is hinged on a reformulation of the reconstruction as the solution to a variational problem. The sign property of…
High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features for nonlinear conservation laws. Entropy stable schemes address this instability by ensuring that physically relevant…
This paper develops high-order well-balanced (WB) energy stable (ES) finite difference schemes for multi-layer (the number of layers $M\geqslant 2$) shallow water equations (SWEs) on both fixed and adaptive moving meshes, extending our…
We introduce two multiscale numerical schemes for the time integration of weakly nonlinear Schr\"odinger equations, built upon the discretization of Picard iterates of the solution. These high-order schemes are designed to achieve high…
Hybrid high-order (HHO) methods are numerical methods characterized by several interesting properties such as local conservativity, geometric flexibility and high-order accuracy. Here, HHO schemes are studied for the space…
We present fourth-order conservative non-splitting semi-Lagrangian (SL) Hermite essentially non-oscillatory (HWENO) schemes for linear transport equations with applications for nonlinear problems including the Vlasov-Poisson system, the…
Different ways of implementing dimension-by-dimension CWENO reconstruction are discussed and the most efficient method is applied to develop a fourth order central scheme for multi-dimensional hyperbolic problems. Fourth order accuracy and…
In this paper, we introduce a high-order tensor-train (TT) finite volume method for the Shallow Water Equations (SWEs). We present the implementation of the $3^{rd}$ order Upwind and the $5^{th}$ order Upwind and WENO reconstruction schemes…
In this paper, we present a high-order unified gas-kinetic scheme (UGKS) using the weighted essentially non-oscillatory with adaptive-order (WENO-AO) method for spatial reconstruction and the two-stage fourth-order scheme for time…
This paper develops the structure-preserving finite volume weighted essentially non-oscillatory (WENO) hybrid schemes for the shallow water equations under the arbitrary Lagrangian-Eulerian (ALE) framework, dubbed as ALE-WENO schemes. The…
This paper focusses on finite volume schemes for solving multilayer diffusion problems. We develop a finite volume method that addresses a deficiency of recently proposed finite volume/difference methods, which consider only a limited…
We present a high-order compact finite difference approach for a class of parabolic partial differential equations with time and space dependent coefficients as well as with mixed second-order derivative terms in $n$ spatial dimensions.…
We present the first high order one-step ADER-WENO finite volume scheme with Adaptive Mesh Refinement (AMR) in multiple space dimensions. High order spatial accuracy is obtained through a WENO reconstruction, while a high order one-step…
In this article we present a modification of the algorithm for data discretized in the point values introduced in [S. Amat, J. Ruiz, C.-W. Shu, On a new WENO algorithm of order 2r with improved accuracy close to discontinuities, App. Math.…
In an attempt to investigate the structures of ultra-relativistic jets injected into the intracluster medium (ICM) and the associated flow dynamics, such as shocks, velocity shear, and turbulence, we have developed a new special…
Higher-order numerical methods are used to find accurate numerical solutions to hyperbolic partial differential equations and equations of transport type. Limiting is required to either converge to the correct type of solution or to adhere…
In this paper, we utilize the maximum-principle-preserving flux limiting technique, originally designed for high order weighted essentially non-oscillatory (WENO) methods for scalar hyperbolic conservation laws, to develop a class of high…
This paper presents high-order numerical methods for solving boundary value problems associated with the Lane-Emden equation, which frequently arises in astrophysics and various nonlinear models. A major challenge in studying this equation…
A large toolbox of numerical schemes for dispersive equations has been established, based on different discretization techniques such as discretizing the variation-of-constants formula (e.g., exponential integrators) or splitting the full…